Geometry is study of shapes you see around you everyday. There are some basic concepts you must understand such as point, line, segment, ray, and angle.
GeometrySketchPadActivities
Assignment
Description
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A
Geometry Sketch pad is used to explore various concepts in geometry
This lesson is based on the Triangle Classification problem,
in which students attempt to classify the triangles formed in a
plane when a randomly selected point is connected to the
endpoints of a given line segment
**Corner to Corner**
Exploring Quadrilaterals, Diagonals, and the Pythagorean Theorem Lesson 1 - Squares, Diagonals, and Square Roots
Students explore the relationship between the lengths of the sides and diagonals of a square. Students will use their discoveries to predict the diagonal length of any square. Lesson 2 - Exploring Diagonals and the Pythagorean Theorem
Students further explore square roots using the diagonals of rectangles. Using measurement, students will discover a method for finding the diagonal of any rectangle when the length and width are known, which leads to the Pythagorean Theorem.
Students identify and classify polygons according to various attributes. They then sort the polygons in Venn Diagrams, according to these attributes. Extensions to fundamental ideas about probability and statistics are also included. This lesson was adapted from an article written by Carol G. Williams, which appeared in the March‑April 1998 edition of Mathematics Teaching in the Middle School
Students hear geometry terminology around them every day. By playing the games in this lesson, students use their knowledge regarding regular and irregular polygons to explore the properties of the shapes and learn new vocabulary when identifying characteristics of shapes.
You are the owner of five pizzerias in the town of Squaresville. To ensure minimal delivery times, you devise a system in which customers call a central phone number and get transferred to the pizzeria that is closest to them. How should you divide the town into five regions so that every house receives delivery from the closest pizzeria? Also, how many people should staff each location based on coverage area?
City of Hartford is planning a new construction project to meet the need of growing population, increase revenue for the city, and to improve unemployment rate. After several considerations the construction committee has decided to construct various buildings on the vacant land across the Putnam highway and I-91 in the city of Hartford.
You are designing a garden bed, to allow people to grow fresh vegetables, flowers, fruit and herbs year round, with minimal extra heating or cooling. Your design needs to be well planned out in order to maximize the area while utilizing all material. Support all reasoning through sound mathematical evidence.
Your goal is to construct a kite from scratch using the properties of kites you learned in geometry class. There are various types of kites but your kite should be the shape of rhombus. You may use any resource available to you including the internet, library to find direction on building a kite.
If a tree could talk, we could ask it how old it is. Here is a mathematical way to estimate the age of your schoolyard trees. Students will measure circumference of trees in order to find diameter and calculate age of local trees using a growth rate table.
**The Giant Cookie Dilemma**
Dividing a Circle in Half by Constructing Concentric Circles
Students explore two different methods for dividing the area of a circle in half,one of which uses concentric circles. The first assumption that many students make is that half of the radius will yield a circle with half the area.
This is not true, and it surprises students. In this lesson, students
investigate the optimal radius length to divide the area of a circle evenly
between an inner circle and an outer ring.
**Circle Packing** Lesson 1 - Soda Cans
Soda cans are often packaged in rectangular arrays, but more efficient arrangements
that require less packaging material are possible. In this lesson, students investigate
various designs for packaging soda cans and use geometry to analyze their designs. Lesson 2 - Soda Rack
In the previous lesson, students considered an arrangement of cans in which the
cans were placed on a shelf. In this lesson, students consider the arrangement of
cans placed in a bin with two vertical sides, discover an interesting result, and
prove that the result is true. Lesson 3 - Circle Packing and Curvature
An important idea in advanced mathematics is curvature, the amount by
which a geometric object deviates from being flat. Mathematicians study the
curvature of advanced curves and three-dimensional shapes. In this lesson,
students investigate the curvature of circles.
Students will identify and classify reflections and symmetries in figures and patterns. They will also create frieze patterns from each of the seven classes using the supplemental activity sheets.
**What’s Regular About Tessellations?**
Tiling the Plane with Regular Polygons
In this lesson, students explore regular and semi-regular tessellations. Students use manipulative to discover which regular polygons will tessellate and which will not. Students will use geometry and measurement to investigate the three regular and eight semi-regular tessellations.
You are to create your own tessellation masterpiece. Your tessellation will be created based on specific criteria. You MUST follow the guidelines given in order to receive full credit.
This lesson focuses on using Venn diagrams to explore direct, indirect,
and transitive reasoning. It was adapted from the article "A Visual
Approach to Deductive Reasoning" by Frances Van Dyke, which appeared in the September 1995 issue of the //Mathematics Teacher// journal.
Geometry Sketch Pad Activities
Assignment
Description
Source
Unit 0: Basic of Geometry and Resources
Assignment
Description
Source
SA and volume formula
Unit 1: Points, Segment, Ray, Line, and Angles
Assignment
Description
Source
Unit 2: Triangles
Assignment
Description
Source
Triangle classification:
This lesson is based on the Triangle Classification problem,in which students attempt to classify the triangles formed in a
plane when a randomly selected point is connected to the
endpoints of a given line segment
Triangle classification online tool
All expenses paid Activity sheet
Map is not drawn to scale Activity Sheet
Central Park & Manhattan MAP
Map is not drawn to scale KEY
Subway map of Manhattan
Unit 3: Right Triangle and Pythagorean theorem
Assignment
Description
Source
Exploring Quadrilaterals, Diagonals, and the Pythagorean Theorem
Lesson 1 - Squares, Diagonals, and Square Roots
Students explore the relationship between the lengths of the sides and diagonals of a square. Students will use their discoveries to predict the diagonal length of any square.
Lesson 2 - Exploring Diagonals and the Pythagorean Theorem
Students further explore square roots using the diagonals of rectangles. Using measurement, students will discover a method for finding the diagonal of any rectangle when the length and width are known, which leads to the Pythagorean Theorem.
Square side and diagonal Activity Sheet
Rectangles and diagonal Activity Sheet
Unit 4: Quadrilaterals and their properties
Assignment
Description
Source
Sorting Polygon:
Students identify and classify polygons according to various attributes. They then sort the polygons in Venn Diagrams, according to these attributes. Extensions to fundamental ideas about probability and statistics are also included. This lesson was adapted from an article written by Carol G. Williams, which appeared in the March‑April 1998 edition of Mathematics Teaching in the Middle SchoolShape Activity Sheet
Sorting Cards
Shape up:
Students hear geometry terminology around them every day. By playing the games in this lesson, students use their knowledge regarding regular and irregular polygons to explore the properties of the shapes and learn new vocabulary when identifying characteristics of shapes.Cutout shapes
Shape sorter tool
Shape up activity Sheet
Shape Up Characteristics Activity Sheet
Shape up sorting chart
Using Multiple Strategies to Solve a Problem Involving the Area of Parallelograms
Pizza Parlor Proximity Overhead
Regions for two pizzerias
Regions for three pizzerias
Regions for four pizzerias
Regions for five pizzerias
Diagonal and quadrilaterals Activity Sheet
Game Rules
Game Cards
Game Pieces
Discovering the Polygon Angle Sum Formula through Investigation
Angle sum tool
Adding it All Up Activity Sheet
Adding it All Up Answer KEY
Unit 5: Area of triangle and quadrilaterals
Assignment
Description
Source
Perimeter and Area of composite figures
Project: City Block construction
City of Hartford is planning a new construction project to meet the need of growing population, increase revenue for the city, and to improve unemployment rate. After several considerations the construction committee has decided to construct various buildings on the vacant land across the Putnam highway and I-91 in the city of Hartford.
Project: Building a garden bed:
You are designing a garden bed, to allow people to grow fresh vegetables, flowers, fruit and herbs year round, with minimal extra heating or cooling. Your design needs to be well planned out in order to maximize the area while utilizing all material. Support all reasoning through sound mathematical evidence.Project: Building a kite:
Your goal is to construct a kite from scratch using the properties of kites you learned in geometry class. There are various types of kites but your kite should be the shape of rhombus. You may use any resource available to you including the internet, library to find direction on building a kite.
Learning About Symmetry and Transformation with an Ancient Greek Puzzle, the Stomachion
Archimedes's Puzzle Activity
Unit 6: Surface area and volume
Assignment
Description
Source
Area and volume with examples
Volume of prism
Surface area of cylinder
Volume of cylinder
Surface area of pyramids
Surface area of pyramids
Volume of pyramids and cones
Volume of pyramid and cones
Surface area of pyramids and cones
Volume of cones
Surface area and volume of spheres
SA and Volume of composite figures
Composite worksheet
Surface Area and Volume of Composite figures
Exploring Changing from a Cylinder to a Rectangular Prism while Keeping the Volume Constant
Cubed cans activity
Exploring Volume using Differently Shaped Popcorn Containers
Popcorn Prism anyone?
Popcorn cylinder anyone?
Comparing Cylinders activity sheet
SOLIDS, NETS, AND CROSS SECTIONS
Unit 7: Circle
Assignment
Description
Source
Tree Talk:
If a tree could talk, we could ask it how old it is. Here is a mathematical way to estimate the age of your schoolyard trees. Students will measure circumference of trees in order to find diameter and calculate age of local trees using a growth rate table.
Ranger talk activity
Lumberjack Activity
Ranger talk table
Lumberjack table
Tree rings overhead
Dividing a Circle in Half by Constructing Concentric Circles
Students explore two different methods for dividing the area of a circle in half,one of which uses concentric circles. The first assumption that many students make is that half of the radius will yield a circle with half the area.
This is not true, and it surprises students. In this lesson, students
investigate the optimal radius length to divide the area of a circle evenly
between an inner circle and an outer ring.
Fair Share Activity Sheet
Giant cookie dilemma Activity Sheet
Giant Cookie Ratio Overhead
Regulation Dartboard Overhead
Hitting your mark Activity Sheet
Hitting your mark Answer KEY
Lesson 1 - Soda Cans
Soda cans are often packaged in rectangular arrays, but more efficient arrangements
that require less packaging material are possible. In this lesson, students investigate
various designs for packaging soda cans and use geometry to analyze their designs.
Lesson 2 - Soda Rack
In the previous lesson, students considered an arrangement of cans in which the
cans were placed on a shelf. In this lesson, students consider the arrangement of
cans placed in a bin with two vertical sides, discover an interesting result, and
prove that the result is true.
Lesson 3 - Circle Packing and Curvature
An important idea in advanced mathematics is curvature, the amount by
which a geometric object deviates from being flat. Mathematicians study the
curvature of advanced curves and three-dimensional shapes. In this lesson,
students investigate the curvature of circles.
Soda Can activity Sheet
Soda Can
online Activity
Circle Packing Activity
Unit 8: Transformation and Pattern
Assignment
Description
Source
Investigating Rotations and Their Properties
Investigating Reflections and Their Properties
Investigating Translations and Their Properties
Investigating Glide Reflections and Their Properties
Classifying Transformation:
Students will identify and classify reflections and symmetries in figures and patterns. They will also create frieze patterns from each of the seven classes using the supplemental activity sheets.
Classify Symmetry
Tiling the Plane with Regular Polygons
In this lesson, students explore regular and semi-regular tessellations. Students use manipulative to discover which regular polygons will tessellate and which will not. Students will use geometry and measurement to investigate the three regular and eight semi-regular tessellations.
Tessellation tool
Whats regular about this polygon overhead
Whats regular about this polygon activity
Regular polygon activity Sheet
Tessellation project:
You are to create your own tessellation masterpiece. Your tessellation will be created based on specific criteria. You MUST follow the guidelines given in order to receive full credit.Tessellation project researched base
Shape template Activity Sheet
Student Activity Sheet
Shape Template
Unit 9: Logic, Proofs, and Induction reasoning.
Assignment
Description
Source
Using a Visual Approach to Direct, Indirect, and Transitive Reasoning
This lesson focuses on using Venn diagrams to explore direct, indirect,
and transitive reasoning. It was adapted from the article "A Visual
Approach to Deductive Reasoning" by Frances Van Dyke, which appeared in the September 1995 issue of the //Mathematics Teacher// journal.
Direct reasoning activity
Indirect reasoning activity
Transitive Reasoning Activity
Valid or invalid Activity
Reference Sheet
Games
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/line_shoot.htm Game on identifying Point, Segment, Line, Ray